Comments on some suggested speakers

Matthias Aschenbrenner or Lou van den Dries (a lot of recent work on Hardy fields) 

Annette Bachmayr (Differential Galois Theory) 

Moulay Barkatou or Suzy Maddah (computing normal forms) 

Jason Bell (Mahler equations and combinatorics) 

Modeling of biological system. Boulier and his co-worker could make  
a contribution. 

One of the suggestions is Victor Buchstaber from Steklov Institute of Mathematics, Moscow. 
His background is algebraic topology, but recently he has been involved in the study of Lie algebroids which are very close to the differential algebra community interests (in particularly Ovchinnikov, Cassidy, ...). He is above 70 years old, a (corresponding) member of the Russian academy of Sciences and a very good speaker. 

John C. Butcher: One area that I recently became aware of is Butcher group (see https://en.wikipedia.org/wiki/Butcher_group). My attention was drawn to this area (and I was totally ignorant of its connection to differential algebra) by a KSDA talk on Runge-Kutta methods of higher orders (7,8,9,10,...). RK methods are for numerical integration of differential equations, with the goal to control the round-off and propagation errors due to smaller step size in time. The methods are derived by solving what has been known as the Butcher equations (an algebraic system). All this is rather straightforward, but I was intriqued by the connections laid out in the Wiki page above. For example, its relation with differential and rooted trees and renormalization of QFT. 
John C. Butcher is still active (he is 83): http://jcbutcher.com  He recently attended two conferences, one in honor of him specifically: Honoring John Butcher on the occasion of his career on Numerical Analysis and Applied Mathematics (http://icnaam.org), the other is an invited talk at ETH Seminar; both took place just before DART VII. So I believe it is reasonable to consider inviting him to introduce Butcher group and its ramifications at DART 8. 

Guy Casale or David Blasquez Sanz (connections with differential geometry and Malgrange Galois theory) 

Shaoshi Chen, has been make many progresses on creative telescoping and 
many other related topics. In particular, a conjecture of Zeilberger was solved. 

Computer tools. One may think of packages designed by Chyzak 
in Maple Mgfun or Ore_algebra, of Boulier's BLAD library. There are 
also a lot of possibilities in Van Der Hoeven's Mathemagix.  

On may think of a session devoted to implementations. 
Ruyong Feng, has made major progresses on computation of Galois groups 
and the related inverse problems for differential and difference linear equations.  

Celestrial mechanics. I think that we may have some obvious common  
interests. Jacques Laskar would be a good invited speaker.    

Rahim Moosa (model theoretic approach to differential equations, although he was a principal speaker at DART VI) 

First integrals. Jean Moulin-Ollagnier, Jean-Marie Strelcyn, Andrzei Nowicki 

Differential invariants, Cartan method. Michel Petitot (perhaps not  
the best speaker in english...) Évelyne Hubert 

Another suggestion is  Omar Leon Sanchez, who has now moved to Manchester for a postdoc position working with Tressl. 

Alban Quadrat has developped important methods related to modules 
over PD operators rings. 

Analytic combinatorics. Bruno Salvy, Frédéric Chyzak, Alin Bostan ... 

Jacques Sauloy (analytic theory of q-difference equations) 

Differential Galois theory or singular initial value problems: 
Matthias Seiß

I am sure the "obvious" recommendations would include: Michael Singer, Alexey Ovchinnikov, Phyllis Cassidy, Anand Pillay, Alexandru Buium, etc, etc. Another set of "obvious" speakers, whose presence is not felt strongly at DART VII, would include Li Guo, Markus Rosenkranz (and Li Guo would be able to recommend more from this area---not just for Rota-Baxter type algebras, but also operads, splitting of associativity, etc.) 

Marcus Tressl (Manchester).  He has done interesting work about model companions of differential fields, which is maybe worth popularizing among the differential algebra community.  

Algebraic methods for dynamical systems: 
Sebastian Walcher and his group (in particular, Niklas Kruff) 

Differential Galois theory: 
Jacques-Arthur Weyl
Michael Wibmer

Chun-Ming Yuan, has initiated the study of binomial difference ideals 
and difference toric varieties, both ordinary and partial case 

Algebraic Systems Theory: 
Eva Zerz and her group (in particular Johannes Nüssle) 
Ulrich Oberst and his group (in particular, Martin Scheicher) 
Alban Quadrat
Daniel Robertz

Yi Zhang. His paper on the contraction of Ore ideals received a distinguished student author award at ISSAC 2016, and have made some progress on desingularization of D-finite systems recently.  

Additional topics and suggestions

Another area that should be included, in my opinion, is Hybrid Automata Theory, where a hybrid automaton is a finite state machine with a finite set of continuous variables whose values are described by a set of ordinary differential equations. (https://en.wikipedia.org/wiki/Hybrid_automaton). Michael Singer's talk at DART VII touched upon Automata Theory. The subject of hybrid automata and differential automata has been studied for at least two decades. It is intimately related to dynamical systems and formal verifications. 

There is a field called algebraic analysis (or microlocal analysis) originated in works by Sato and Kashiwara. They study differential equations combining complex analysis, sheaf theory, and D-modules. I do not know much about applications, but as far as I understood, these techniques allow to generalize Cauchy-Kowalevski theorem and play an important role in the computation of the index of a differential operator. 

I think it might be interesting to invite somebody from this field to DART, maybe even ask to give couple of survey talks. 

I found only one survey, but it is quite formal and does not include applications: 
https://arxiv.org/pdf/1206.1435v3.pdf  (more theoretic) 
Here are some people in the field 
http://www.kurims.kyoto-u.ac.jp/~kenkyubu/kashiwara/
https://webusers.imj-prg.fr/~pierre.schapira/
http://docenti.math.unipd.it/dagnolo/coordinates.php?lan=0
Maybe you or members of PC know more about the subject and can give some recommendations.